Lottery

I got thinking about the lottery. I was wondering if there was a way to guarantee a win. The only legal way to do that is to buy a ticket corresponding to every possible numeric combination.

So with the New Jersey lottery:
There are 5 numbers (1-56) plus the "gold ball" (1-46).To match the first 5 its 56 x 55 x 54 x 53 x 52 (1:56 chance to get the 1st number right, 1:55 chance to get the second number, etc.)Then to get the "gold ball" its just multiplying by 46 (1:46 chance). So for the first five its 458,377,920 possible combinations. But because it doesn't matter what order the numbers are in we divide by 5 factorial (number of numbers chosen) which gives us 3,819,816. Then multiply that by the "gold ball" so 3,819,816 x 46 = 175,711,536 possibilities.

So in order to play every possible ticket you need $175,711,536. To make it easier you could team up with people and each put in like $100-$1000. Say you do $1000 per person, then you need 175,712 people. So that's about Daytona Speedway plus about 8000. So it's not really out of hand yet (sort of).

Taking the cash prize actually decreases by over half since all the taxes are taken out at once. It's about 60% taken out. So to break even in the lottery you need the advertised cash prize to be about $292,852,560. The largest mega million jack pot in history is $315 million. So with taxes taken out (25% federal, NJ residents are exempt from paying NJ state tax on lottery winnings), the cash prize is about $236.25 million. Tallied up among all the people who played that's $1,344.52 a person. Which means each ticket made 34 cents. Awesome... simply awesome...